Semirigid elliptical waveguide

ABSTRACT

A FLEXIBLE RADIO FREQUENCY TRANSMISSION LINE OF THE WAVEGUIDE-TYPE CONSISTING OF A WAVEGUIDE STRUCTURE OF SEMIRIGID CONDUCTIVE MATERIAL HAVING A UNIFORM LONGITUDINAL PROFILE WHOSE INTERIOR CROSS SECTION IS DEFINED BY AN ELLIPSE AND WHOSE EXTERIOR CROSS SECTION IS DEFINED BY THE INTERSECTION OF A CIRCLE AND RECTANGLE, THE RECTANGULAR SIDES BEING PARALLEL TO THE MAJOR DIAMETER OF THE ELLIPSE AND TRANSITIONING AT BOTH ENDS INTO SECTORS OF THE CIRCLE.

United States Patent [72] Inventors Lewis A. Bondon 90 Yantacaw BrookRoad, Upper Montclair, NJ. 07043; David L. Bondon. Northgate Apts.#107K. One Mile Road, Cranbury, NJ. 08512 [21] Appl. No. 681,179 [221Filed Nov. 7, 1967 [45] Patented June 28, 1971 [54] SEMI-RIGIDELLIPTICAL WAVEGUIDE 6 China, 9 Drawing Figs.

52 1 0.5. CI. 333/95, 138/177, 138/118 511 lnt.Cl. H01p3/l4 [50] Field01 Search ..333/95 (A), 95

[56] References Cited UNITED STATES PATENTS 3,304,521 2/1967 Freibergset al. 333/95 3,444,487 5/l969 Krank OTHER REFERENCES Valenzuela, G. R.,The Cut-Off Wavelengths and Power- Voltage lmpedances of CompositeWaveguides for the Fundamental Mode" Technical Report No. AF-87, TheJohns Hopkins University Radiation Laboratory, Baltimore, Md., May 1961Primary Examiner-Herman Karl Saalbach Assistant ExaminerSaxfieldChatmon, Jr. Attorney-Hopgood and Calimafde ABSTRACT: A flexible radiofrequency transmission line of the waveguide-type consisting of awaveguide structure of semirigid conductive material having a uniformlongitudinal profile whose interior cross section is defined by anellipse and whose exterior cross section is defined by the intersectionof av circle and rectangle, the rectangular sides being parallel to themajor diameter of the ellipse and transitioning at both ends intosectors of the circle.

I SEMI-RIGID ELLIPTICAL WAVEGUIDE BACKGROUND OF THE INVENTION Waveguidesmay be either open or closed structures. In the former, the field in thecross-sectional plane of the guide extends to infinity. In the latter,the field will be confined to a defined region. Parallel wiretransmission line represents an open waveguide, and coaxial and hollowmetal pipe are examples of closed waveguides. This application isconcerned with waveguides of the hollow, metal pipe-type, and the termwaveguide" (or guide") when used herein may be deemed to be sorestricted.

To date, the most efficient form of microwave transmission media iswaveguide. and in particular, circular waveguide. When properlydesigned. the performance characteristics of this type of transmissionline are practically unmatched. In most cases, however. optimumperformance criteria is costly and this is particularly true of circularwaveguide.

For propagation of energy at microwave frequencies through hollow metaltubes, a number of different waves are available known as TE and TMwaves. A TE wave is a transverse electric wave, sometimes called an Hwave, characterized by the fact that the electric vector (the E vector)is always perpendicular to the direction of propagation. That is, thereis no electric vector longitudinally in the pipe. TM, or transversemagnetic, waves, also called E waves, are characterized by the fact thatthe magnetic vector (H vector) is always perpendicular to the directionof propagation and there is no magnetic component longitudinally in thepipe.

The solution for the field configuration in waveguides is characterizedby the presence (after the designation TE or TM) or integers mand nwhich take on separate values from or 1 to infinity. Only a limitednumber of these different m, n modes can be propagated depending uponthe dimensions of the guide and the frequency of the excitation.

In circular waveguide, to provide the lowest attenuation, the TE modemust be launched and maintained throughout the system. Any dimensionaldiscontinuities in the circular waveguide will generate higher ordermodes which significantly degrade the performance of the waveguide.Accordingly, in order to insure purity, circular guide and itsassociated components must be constructed with extreme accuracy. Wherebends are required, they are difficult and costly to obtain and filtersare generally inserted in the system to control unwanted modes.

In recent years, the considerations of attenuation vis-a-vis cost havegenerally dictated the use of 'rigid rectangular waveguide. Rectangularwaveguide installations, like circular waveguides, however, must meetdesign criteria which almost always require the insertion of bends ortwists in the guide to adopt the physical positioning of the systemitself. In order to insure that such bends and twists do not introducediscontinuities which would create modes adversely affecting the system,the bends are separately constructed with great precision and with everyeffort being expended to maintain the interior dimensional integrity ofthe bent section. Moreover, depending upon the plane in which the bendis taking place, separate types of bends are required to accommodate Eand H plane directional changes.

Separate bent waveguide sections are hardly a completely satisfactoryanswer since their use allows practically no adjust ment in theconfiguration of the final assembly, nor does it permit simple fieldmodification of element positions.

Thus, there has sprung into being a family of flexible waveguides whosephysical characteristics vary widely. One conventional type of flexiblewaveguide is constructed of a continuous spiral of interlocking stripsexternally covered with rubber. Another conventional-type flexible guideincludes a continuous metal corrugated to permit flexing; recently,elliptical corrugated guide has been introduced. Corrugated guide offersthe advantage of no leakage where the guide is to be pressurized. Stillanother type has a spiralled periphery, which, once the finalconfiguration has been achieved, is soldered, brazed or welded.

The foregoing flexible guide structures, however, present severaldisadvantages. Primarily, the attenuation tends to be extremely high asopposed to, for example, rectangular sections into which they terminate,and is therefore prohibitive for long runs. The brazing, welding orsoldering operations are in themselves extremely inconvenient, and theresultant structure will not withstand torsional stresses which willpart the seams. Corrugated waveguide has a high fatigue factor and thechances of crystallization are relatively high; the system tending to bede-ruggedized by this weak link.

' Moreover, each junction point where a flexible waveguide element meetsa rigid element invariably, unless very closely toleranced, produces adiscontinuity giving rise to the injection of higher order modes whichdisadvantageously affect the .output.

OBJECTS OF THE INVENTION It is the object of this invention to provide aradio frequency transmission media of the waveguide-type which may betwisted and fonned with comparative ease (semirigid) into anyinstallation configuration, and which is sufficiently low in attenuationso that it may replace not only flexible waveguide but also the rigidguide, thereby reducing the number of discontinuities caused byjunctions.

It is a further object of this invention to provide a structure of theforegoing type which may be supplied in continuous reeled lengths forrapid field assembly.

It is a further object of this invention to provide a waveguidestructure which has greater width and requires a minimum number of sizesto cover frequency ranges in which other types of waveguide arecurrently being employed.

It is a further object of this invention to provide a waveguidestructure which is integral longitudinally and has no welded seams tofail and cause pressurizationleaks.

It is a further object of this invention to provide a flexible orsemirigid guide with a low fatigue factor which minimizes its chance ofcrystallization and which will take substantial twist moments withoutfailure.

It is a further object of this invention to provide a flexible waveguidewith electrical characteristics at least equivalent to those now foundin rigid rectangular waveguide.

it is a still further object of this invention to provide a flexiblewaveguide which may be economically manufactured by accepted fabricationtechniques and which is capable of being simply and expeditiouslyterminated into rectangular and/or circular waveguide sections.

A BRIEF SUMMARY OF THE INVENTION Briefly, the invention is predicatedupon the concept of providing a waveguiding structure of semirigidmaterial with a longitudinally uniform profile defined on the interiorcross section by an ellipse and in thickness by a virtual trussconfiguration which maintains the inside elliptical integrity when thewaveguide is either bent or twisted by allowing the metal to yieldwithout interior distortion of the ellipse.

The above mentioned and other features and objects of this invention andthe manner of attaining them will become more apparent and the inventionitself will best be understood by reference to the following descriptionof an embodiment of the invention taken in conjunction with theaccompanying drawings, the description of which follows.

DESCRIPTION OF VIEWS OF THE DRAWINGS FIG. I is a perspectiveillustration of one embodiment of waveguide according to the invention.

FIG. 2 shows the elliptical coordinate system.

FIG. 3 is a graph of the cutoff wavelength as a function of theeccentricity of the 0H, mode.

FIG. 4 is a graph of wavelength, in elliptical guide, versus frequency.

FIG. 5 shows the field configuration of the eH wave in elliptical pipehaving an eccentricity of 0.75.

FIG. 6 is a graph of the attenuation in an air-filled copper pipe.

FIG. 7 illustrates the comparative attenuation data for rectangularwaveguide as opposed to the waveguide according to the invention.

FIG. 8 schematically shows how the exterior configuration of thewaveguide may be defined by geometric figures, and

FIG. 9 shall be used to illustrate the theoretical force linesencountered in bending.

DETAILED DESCRIPTION OF THE INVENTION In order to more fully appreciatethe invention and its employment in the radio frequency field, a briefexamination of the field configurations in hollow conducting pipes ofelliptical cross section is desirable.

The coordinate system for an ellipse such as is under consideration isgiven in FIG. 2. The elliptic coordinate system may be defined in termsof a right-hand Cartesian system by the equations The contour surfacesof constant I are confocal elliptic cylinders, and those of constant nare confocal hyperbolic cylinders. The constant q represents half thedistance between the foci. One of the confocal elliptic cylinders withis assumed to coincide with the inner boundary of the elliptic pipe, andthe x axis coincides with its longitudinal axis. The major and minoraxes of the boundary ellipse are q cosh and q sinh 9,, respectively, adits eccentricity, e,95 given by l/cosh The Maxwell equations for a wavein an elliptical pipe can be employed in the usual manner to derive thewave equations for E, and H,. After separating the variables {and n, theequations are known as the Mathieu equations, and their solutions as theMathieu functions. A more detailed examination of the mathematicsinvolved may be had be resort to "Electromagnetic Waves in EllipticHollow Pipes of Metal," Lan .Ien Chu, Journal ofApplied Physics, Vol. 9,pp. 583--59l, Sept. I938. As enunciated by Mr. Chu, an H or E wave in anelliptic pipe may be designated by the prescript e or indicating thatthe wave is described by either the even or the odd Mathieu functions. Adouble subscript nm is also employed in the usual manner where n denotesthe order of the Mathieu function and m denotes the particular route.For present purposes, it is necessary only to investigate the six lowestorder waves. Since this is the first route, the distinguishingcharacteristic m=l will be omitted and the six lowest order waves may bedesignated eH eH,, 0H,, 2E eE and 05,.

From extensive analysis of various elliptical configurations andtransitions from rectangular and circular guide, it appears that thedominant mode transmitted in elliptical waveguide is the eH, mode.Accordingly, references hereinafter shall be made almost exclusively tothis mode. Should such assumption prove to be incorrect, the generalconcepts and fonnulae derived are nevertheless value and may be resortedto in considerations of the newly assumed dominant mode.

Applying the general consideration that when the phase constant is 0,waves cannot travel through the pipe; the value of the wavelength forwhich the phase constant is 0, commonly called the critical or cutoffwavelength, A may be determined from a Bessel-Fourier series expansionfor the Mathieu functions.

In FIG. 3, the ratio of A is plotted for the eH mode for various degreesof eccentricity; S is the peripheral length of the guide.

From knowledge of the cutoff wavelength, the guide wavelength may beobtained using standard procedure. A graphic illustration of thewavelength in elliptical guide may be seen by reference to FIG. 4 whichshall be referred to again hereafter.

The field configuration of the 2H, wave may be seen in FIG. where thesolid lines represent the electric field and the dashed lines themagnetic field. Where the conductivity of the metal pipe is assumed tobe finite, the field inside the pipe obviously distorts from the shapeshown, since the finiteness of the conductivity requires differentboundary considerations.

However, if the conductivity is assumed to be very large, the wave maybe assumed to take the form shown with very little deviation.

The calculation of the attenuation constants may be made upon the basisof the usual boundary considerations for metals of high conductivity,the solution of the longitudinal fields, the integration ofthe Poyntingvector to determine the power loss into the metal, and a determinationof the total power transmitted through the pipe; the latter by usingfield expressions of a perfectly conducting pipe.

FIG. 6 illustrates the attenuation of the waves for the eH, mode as afunction of GHz. with varying degrees of eccentricity. FIG. 7 will bereferred to hereinafter, and illustrates comparative attenuation datafor a rectangular waveguide and the waveguide according to theinvention.

Having briefly outlined the electrical considerations andcharacteristics of elliptical waveguide, an analysis shall now be madeof the physical embodiment of the invention which gives rise to anelliptical waveguide capable of permitting bends and twists withoutdistortion.

FIG. I illustrates one embodiment of the waveguide according to theinvention. As may be seen, the interior of the guide is elliptical incross section having a major diameter a and a minor diameter b. Theguide exterior may be visualized as shown in FIG. 8 as a combination ofarectangle e and circlef. The width of the rectangle is greater than theminor ellipse diameter b by an amount 20, and the circle diameter isgreater than the major ellipse diameter a by amount 2d.

The exterior guide shape shown simultaneously resolves severalconsiderations. First, the flat sides which are parallel to the majorellipse diameter allow the guide to be precisely indexed where it is tobe transitioned into rectangular waveguide. The circular ends, on theother hand, permit the use ofa proven connector gripping technique nowused to terminate many other types of rftransmission lines withoutbrazing or welding as described in US. Pat. No. 3,010,747. Seals may beadded to the described connector to insure pressurized junctions.

The guide shown in FIG. I may be seen to be longitudinally uniform. Thatis, as one travels down the guide, the profile remains constantvis-a-vis corrugated or seam convoluted flexible waveguide.

The waveguide material is a highly conductive metal which has thefurther attribute of being semirigid. By semirigid is meant a materialwhich can be twisted and bent with comparative ease and has physicalcharacteristics roughly equivalent to that of pure copper or aluminumalloy l0-60 or 10-90; retaining imparted defonnations withoutcrystallizing, cracking or otherwise impairing its characteristics.

10-60 aluminum has been found to be an excellent material for thedescribed use as it may be extruded with an extremely smooth innersurface, as a continuous seamless tube in lengths up to 300 feet ormore; the inner surface may be held at close tolerances; and thefinished waveguide may be easily cut with a hacksaw and filed to asmooth surface to be inserted into its terminating connector.

A waveguide made of -60 aluminum may also be bent (generally twisted aswell) with bare hands in the field without difficulty, and any degree oftwist up to can be made during installation with simple tools. It willwithstand relatively rough field treatment vis-a-vis existing waveguide.The exterior surface may be covered, for example, with an epoxy finishto protect it from pitting and corrosion, if required. For shippingpurposes, the guide may be wound on a drum.

FIG. 9 illustrates how the waveguide according to the inventioninternally distributes bending forces. H and E plane bends, applied tothe waveguide, will result in net efi'ective forces F or F, Regardlessof the direction of the applied force, it will be supported by anarchlike structure which resolves the vertical or horizontal pressure,into diagonal thrusts. Stated differently, regardless of the directionof the application of the force, it is met by an assemblage oftriangular trusses so combined as to form a rigid framework which cannotbe deformed by the application of an exterior force without deformationof one or more of the sides of the particular triangle. As aconsequence, the force is so distributed as to maintain the integrity ofthe internal configuration of the ellipse. Twist moments are similarlyresolved by the truss configuration to maintain the ellipse.

From the foregoing explanation, it may be seen that it is not requisitefor the exterior shape to be precisely that shown in FIG. 1. However,the flat sides do uniquely resolve indexing problems and the circularends resolve termination considerations. With the latter considerationsaside and with different means for joining sections, the external shapemay vary widely so long as the resultant arch contains a virtual trussconfiguration such as shown in FIG. 9 to support the internal ellipticalintegrity. As may be seen from FIG. 9, the selected exterior profileclosely approximates a triangle in each of quadrants g, h, l and] andthus has very little excess material.

The specific preferred profile dimensions for a given frequency andapplication involve considerations of mode stability, attenuation,formability, etc. An exemplary profile which meets the flexibilityrequirements desired and has excellent electrical characteristics in therange 5.0-8.0 GHz. has the following dimensions.

Major ellipse diameter a 1.660 inches Minor ellipse diameter b 1.055inches Thickness c 0. l 25 inches Thickness d 0.220 inches The waveguideweighs 1 lb. 2 oz. per foot and may be bent by hand in the E plane to a24-inch radius, and in the H plane to a 36-inch radius. Using knownmanufacturing techniques. more careful bends may be made at the factoryin the E plane to a 6-inch radius, and in the H plane to a 12-inchradius.

The wavelength and attenuation characteristics of such a guide may beseen by reference to FIGS. 4 and 7, respectively. For purposes ofcomparison, FIG. 7 also includes the attenuation versus frequencyresponse of conventional WR-l 37 rectangular copper waveguide. Anexamination of the graph will reveal that the inventive waveguide evenwhen formed out of 10-60 aluminum is superior to rectangular waveguidemade of copper.

Similar results were obtained vis-a-vis rectangular waveguide withinventive guide having a bandwidth of from 3.7 to 6 GHz. (major diameter2.48 inches, minor diameter 1.56 inches) and also elliptical waveguidehaving a bandwidth from 7.0 to 11.0 GI-Iz. (major diameter 1.830 inchesand minor diameter 1.354 inches).

From the viewpoint of mechanical stability, it has been empiricallyfound preferable to relate the thicknesses d and c roughly by a ratio of2. This ratio, it is theorized, allows greater deformation, within theplastic limits, of the material at the ends of the major diameter wheregreater compression and expansion will take place when bent in the planeof the minor axis.

While bending may result in some distortion of the internal ellipse,this occurs at a point where the elliptical modes have already beenlaunched, and is of minor effect since the gradual alteration of theellipse diameters merely moves the consideration of that mode to aslightly different eccentricity. From FIG. 6, it may be seen that widevariations in eccentricity are possible without destroying orsignificantly aflecting the mode. While FIG. 6 shows in particular theeH, wave, the same holds true for a majority of the modes.

The elliptical waveguide according to the invention satisfies all theobjects delineated above and provides a broad bandwidth waveguide ofexcellent attenuation characteristics which can be manufactured,packaged and assembled with relative ease. No prefabricated bends ortwists are necessary, and the multiple coupling flanges normallyrequired with rectangular guide to join several sections are eliminated.The walls of the guide are sufficiently thick so that it cannot beeasily dented and it will withstand relatively rough handling and permitrapid and economical means for attachment to its supporting structure.The cost of the inventive waveguide is competitive with rectangularwaveguide, yet its bandwidth is greater and its attenuation lower. Whilea flexible guide, the waveguide of the invention is uniquely suitable tohigh gas pressurization which is often a necessary operationalrequirement where high power is to be handled.

The dominant mode in the elliptical guide is, as mentioned, thought tobe the eH, mode which is similar to the TEO mode in rectangularwaveguide or the TE. mode in circular waveguide. The power handlingcapability of the elliptical waveguide is somewhat in excess ofrectangular waveguide but is less than TEO, circular waveguide; however,it requires no mode filtering as does circular waveguide.

One hundred feet of the inventive waveguide for the bandwidth for 5 to 8CH2 and including two transitions to rectangular waveguide exhibit amaximum VSWR of 1.06 with bends of in the E plane of only 18 inches inradius only negligibly affect the VSWR of the line. An E plane bend witha 6-inch radius adds less than a 1.03 VSWR contribution.

While the principles of the invention have been described in connectionwith specific apparatus, it is to be clearly understood that thisdescription is made only by way of example and not as a limitation tothe scope of the invention as set forth in the objects thereof and inthe accompanying claims. For example, while the specific embodimentdescribed has an eccentricity of approximately 0.77, it has been foundthat any eccentricity below 0.8 (that is, 0.8 to 0) exhibits almost allof the characteristics described, and that above 0.8 the desiredattributes rapidly deteriorate.

We claim:

I. A flexible radio frequency transmission media comprising awaveguiding structure of semirigid material having a longitudinallylinear profile when said structure is rectilinear in attitude anddefined on the interior cross section by an ellipse and in thickness bya virtual truss configuration maintaining the inside ellipticalintegrity when the waveguide is either bent or twisted.

2. The transmission media claimed in claim 1 wherein the eccentricity ofthe ellipse is 0.8 or less.

3. The transmission media claimed in claim 1 where the trussconfiguration defines substantially triangular sections in quadrantsdescribed by the elliptical axes.

4. The transmission media claimed in claim 3 where the exterior profileis rectilinear in cross section for a predetermined length parallel to,and on both sides of, the major elliptical axis.

5. The transmission media claimed in claim 4 wherein the exteriorprofile of the waveguide adjacent the end to the major diameter of theellipse is circular and meets the said rectilinear portion.

6. The transmission media claimed in claim 3 wherein the thickness ofthe waveguide along the major diameter is greater than that along theminor diameter and wherein the ratio is approximately 2 to l.

